20 papers · ranked by Valyu relevance
Benjamin Grimmer, Alex L. Wang
This work considers the design of first-order convex optimization algorithms and convergence proofs. In particular, we consider nonsmooth Lipschitz and smooth problems accessed through a subgradient or gradient oracle, respectively. For the general class of fixed-step first-order methods, prior work on Performance…
Lexiao Lai, Mingzhi Song
We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms dominated by a double summation of step sizes. Consequently, we prove that bounded…
G. C. Bento, J. X. Cruz Neto, J. O. Lopes, I. D. L. Melo
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant optimization algorithms. Motivated by classical Euclidean results and recent advances in…
Evgenii Chzhen, Sholom Schechtman
We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata) on which the function is smooth; ii) a global projection formula for Clarke…
Kiyuob Jung
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical methods that use specular gradients in subgradient methods. We prove the…
Morteza Rahimi, Masoud Ahookhosh
We introduce the class of relatively weakly convex functions, which extends the classical notion of weak convexity by measuring nonconvexity relative to a distance-generating function. We investigate the fundamental properties of this function class, establishing characterization results, calculus rules, and…
Margarita Preobrazhenskaia, Makar Sidorov, Igor Preobrazhenskii, Eduard Gorbunov
We study the convergence of the last iterate (i.e., the $(N+1)$-th iterate) of the AdaGrad method. Although AdaGrad -- an adaptive subgradient method -- underpins a wide class of algorithms, most existing convergence analyses focus on averaged (or best) iterates. We derive worst-case upper bounds on the suboptimality…
Mohamed A. Mokhtar, Mohamed Fathy, Yasser A. Dahab, Emad A. Sayed
In modern machine learning, optimization algorithms are crucial; they steer the training process by skillfully navigating through complex, high-dimensional loss landscapes. Among these, stochastic gradient descent with momentum (SGDM) is widely adopted for its ability to accelerate convergence in shallow regions.…
Lulu He, Yanan Du, Jianchao Bai
The conjugate gradient method is widely recognized as a foundational technique for large-scale unconstrained optimization. In this work, we introduce an Accelerated Stochastic Conjugate Gradient (ASCG) algorithm, specifically designed for a class of convex empirical risk minimization problems. The proposed ASCG method…
Amir Hossein Salehi Shayegan
In this work, we present a solution to the critical limitation of qubit capacity in near-term quantum hardware by giving a hybrid framework that integrates the spectral element method (SEM) with distributed quantum computing. Using domain decomposition techniques, the additive and multiplicative Schwarz methods, the…
Yan Xia, Dandan Li, Songhua Wang, Mohamed Kamel Riahi
In this paper, a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations is proposed by integrating both hyperplane projection and hybrid techniques. The key features of this method are as follows: (1) It is characterized by a low storage requirement and relies solely on…
Zelin Pei, Xiaoyu He, Yi Pan, Baichun Peng + 2 more
Black-box stochastic optimization involves sampling in both the solution and data spaces. Traditional variance reduction methods mainly designed for reducing the data sampling noise may suffer from slow convergence if the noise in the solution space is poorly handled. In this paper, we present a novel zeroth-order…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
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We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
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Finding the most stable adsorption geometry of a flexible molecule on a catalytic surface remains a key challenge due to the high dimensionality and ruggedness of the potential energy surface. We present a Gradient-Enhanced Genetic Algorithm (GE-GA) for the global optimization of adsorbate–surface configurations…
Kabiru Ahmed, Hatem E. Semary, Asmaa S. Al-Moisheer, Sulaiman M. Ibrahim + 5 more
This paper presents a new iterative method with a restart feature for solving constrained system of nonlinear monotone equations. The scheme, which is a double-parameter method, was initiated by considering a positive-definite adaptation of the quasi-Newton update proposed by Andrei (J. Comput. Appl. Math. 332, 26-44…
Authors not listed
Machine olfaction—the artificial replication of the sense of smell—faces significant challenges due to the absence of large, standardized training datasets. Unlike vision, language, and audio models, which benefit from extensive corpora such as ImageNet, GLUE, and AudioSet, olfaction lacks scaled equivalents and…
Rudra Prakash, Shaunak Sen
The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To…
Stephan Grein, David R. Penas, Daniel Weindl, Polina Lakrisenko + 2 more
Dynamic models are central to the computational life sciences but typically contain unknown parameters that must be inferred from experimental data. High-throughput measurements have made this task increasingly challenging, yielding high-dimensional search spaces and non-convex objectives with many local optima. This…
Saima Bibi, Syeda Tehmina Ejaz
In numerical methods, fine mesh sizes are often necessary to obtain highly accurate solutions of the differential equations and this increases the memory consumption and decreases the efficiency of the calculation. This paper presents a subdivision collocation algorithm of time-fractional advection diffusion equation…